HAMILTON VARIATIONAL PRINCIPLE AND ECOLOGICAL MODELS

In physics, dynamical equations are often derived from a quantity know n as the ''action'' using Hamilton's variational principle. In effect, the action provides a convenient and elegant summary of the propertie s of a system. In this paper the use of Hamilton's variational princip le to derive ecological models is discussed, using the logistic equati on as a simple example. A second model which displays contrasting dyna mical behaviour is also considered. The action is interpreted as the s um of a term describing the intrinsic dynamical behaviour of the popul ation (e.g. exponential growth) and a term describing environmental fa ctors. This approach shifts the emphasis away from system behaviour as a basis for modelling. Instead the emphasis is on factors affecting t he system, which consequently determine its behaviour. Models based on second-order differential equations arise naturally in this approach.